A Concurrent Multi-Scale Modeling of Heterogeneous Nano-Structures

Jahanbakhshi, Farzaneh | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 44068 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Khoei, Amir Reza
  7. Abstract:
  8. In line with the high computational cost of Molecular Dynamics resulting in restrictions in time and domain, and incompetency of Finite Element method to deal with problems like those consisting of inhomogeneities, where no distinctive constitutive law may be considered, the multi scale methods have extensively settled as an alternative in recent decades. In continuation of preceding studies in the presented research, a concurrent multi scale procedure is employed for coupling MD-FE methods applying Lagrange multiplier approach in order for energy to resemble in transient zone and calculating the stiffness matrix of FE mesh employing the atomic grid laid beneath in order to investigate the mechanical behavior of binary alloys and heterogeneous nano crystalline structures. In the aforesaid method the FE stiffness matrix adopted from the atomic layer underneath is transferred to the FE layer through a linear transformation resulting in solving the equation of motion. Besides, molecular dynamics was implemented to deal with binary alloy problems and heterogeneous F.C.C crystalline structures and also employed in multi scale approach. Lattice parameters for different binary alloys were calculated via minimizing the atomic energy and compared to those of experimental data so as to investigate the integrity of implemented molecular dynamics. As a final point, some examples were studied through
    concurrent coupling of atomic scale and continuum finite element in nano
    structures including inclusions
  9. Keywords:
  10. Concurrent Multi-scale Model ; Rafiitabar-Sutoon Potential Function ; Face Centered Cubic (FCC)Alloy ; Heterogeneous Nanostructures ; Effective Lattice Parameter

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